A048764 Largest factorial <= n.

1, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24

Offset

1,2

References

Krassimir T. Atanassov, On the 43rd and 44th Smarandache Problems, Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, Vol. 5, No. 2 (1999), 86-88.

J. Castillo, Other Smarandache Type Functions: Inferior/Superior Smarandache f-part of x, Smarandache Notions Journal, Vol. 10, No. 1-2-3 (1999), 202-204.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Krassimir T. Atanassov, On Some of Smarandache's Problems.

Li Jie, On the inferior and superior factorial part sequences, in Zhang Wenpeng (ed.), Research on Smarandache Problems in Number Theory (collected papers), 2004, pp. 47-48.

Florentin Smarandache, Only Problems, Not Solutions!.

Formula

a(n) >> n log log n / log n. - Charles R Greathouse IV, Sep 19 2012

From Amiram Eldar, Aug 02 2022: (Start)

Sum_{n>=1} 1/a(n)^m = Sum_{k>=1} k/k!^m (Li Jie, 2004).

In particular:

Sum_{n>=1} 1/a(n)^2 = e (A001113).

Sum_{n>=1} 1/a(n)^3 = BesselI(1,2) (A096789). (End)

Mathematica

Table[k = 1; While[(k + 1)! <= n, k++]; k!, {n, 80}] (* Michael De Vlieger, Aug 30 2016 *)

Prog

(PARI) a(n)=my(t=1, k=1); while(t<=n, t*=k++); t/k \\ Charles R Greathouse IV, Sep 19 2012
(Python)
from sympy import factorial as f
def a(n):
    k=1
    while f(k + 1)<=n: k+=1
    return f(k)
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 21 2017, after Mathematica code

Crossrefs

Cf. A000142, A001113, A096789.

Sequence in context: A116863 A136494 A260188 * A327663 A248782 A038714

Adjacent sequences: A048761 A048762 A048763 * A048765 A048766 A048767

Keyword

nonn,easy

Author

Charles T. Le (charlestle(AT)yahoo.com)

Status

approved